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A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: 20 December 2023 | Viewed by 3567

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Special Issue Editor

Prof. Dr. Mića Stanković

E-Mail Website
Guest Editor

Department of Mathematics, Faculty of Sciences and Mathematics, University of Nis, Niš, Serbia
Interests: Riemannian geometry; spaces of non symmetric affine connection; geodesic mappings; Finsler geometry; infinitesimal bending; almost geodesic mappings; Kahlerian spaces
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue on "Differential Geometry and Its Application". Our intention is to launch a Special Edition of Axioms in which the central theme would be the generalization of Riemann spaces and their mappings.

We wish to provide an opportunity to present the latest achievements in many branches of theoretical and practical studies of mathematics, which are related to the theory of Riemann and generalized Riemann spaces and their mappings.

Among the topics that will be included in this Special Issue, we can consider the following non-exhaustive list: Riemannian Spaces and generalizations, Kenmotsu manifolds, Kaehler manifolds, manifolds with non-symmetric linear connections, cosymplectic manifolds, contact manifolds, statistical manifolds, Minkowski spaces, geodesic mappings, almost geodesic mappings, holomorphically projective mappings, warped product of manifolds, complex space forms, quaternionic space forms, golden manifolds, inequalities, invariants, immersions, etc.

In addition to the above topics, new ideas are also welcome.

In the hope that this initiative will be of interest, we encourage you to submit your current research for inclusion in the Special Issue.

Prof. Dr. Mića Stanković
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

contact manifolds
generalized Riemann spaces
statistical manifolds
Kenmotsu manifolds
Kaehler manifolds
golden manifolds
invariants
immersions
complex space forms
geodesic mappings

Related Special Issue

Differential Geometry and Its Application in Axioms (17 articles)

Published Papers (7 papers)

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Research

14 pages, 514 KiB

Open AccessArticle

Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space

Nadia Alluhaibi

and

Rashad A. Abdel-Baky

Axioms 2023, 12(11), 1022; https://doi.org/10.3390/axioms12111022 - 30 Oct 2023

Viewed by 464

Abstract

A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of [...] Read more.

G_{3}

. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

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18 pages, 787 KiB

Open AccessArticle

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

Areej A. Almoneef

and

Rashad A. Abdel-Baky

Axioms 2023, 12(10), 915; https://doi.org/10.3390/axioms12100915 - 26 Sep 2023

Viewed by 384

Abstract

This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

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11 pages, 313 KiB

Open AccessArticle

A Solitonic Study of Riemannian Manifolds Equipped with a Semi-Symmetric Metric ξ-Connection

Abdul Haseeb

Sudhakar Kumar Chaubey

Fatemah Mofarreh

and

Abdullah Ali H. Ahmadini

Axioms 2023, 12(9), 809; https://doi.org/10.3390/axioms12090809 - 23 Aug 2023

Viewed by 514

Abstract

The aim of this paper is to characterize a Riemannian 3-manifold

M^{3}

equipped with a semi-symmetric metric

ξ

-connection

\tilde{\nabla}

with

ρ

-Einstein and gradient

ρ

-Einstein solitons. The existence of a gradient

ρ

-Einstein soliton in an

M^{3}

admitting [...] Read more.

The aim of this paper is to characterize a Riemannian 3-manifold

M^{3}

equipped with a semi-symmetric metric

ξ

-connection

\tilde{\nabla}

with

ρ

-Einstein and gradient

ρ

-Einstein solitons. The existence of a gradient

ρ

-Einstein soliton in an

M^{3}

admitting

\tilde{\nabla}

is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of

(M^{3}, \tilde{\nabla})

satisfies the Poisson equation

Δ R = \frac{4 (2 - σ - 6 ρ)}{ρ}

. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

17 pages, 356 KiB

Open AccessArticle

η-Ricci–Yamabe Solitons along Riemannian Submersions

and

Axioms 2023, 12(8), 796; https://doi.org/10.3390/axioms12080796 - 17 Aug 2023

Cited by 1 | Viewed by 465

Abstract

In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the

η

-Ricci–Yamabe soliton (

η

-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an

η

-RY soliton, an [...] Read more.

In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the

η

-Ricci–Yamabe soliton (

η

-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an

η

-RY soliton, an

η

-Ricci soliton, and an

η

-Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an

η

-RY soliton, an

η

-Ricci soliton, an

η

-Yamabe soliton, or a quasi-Yamabe soliton. We deduce a Poisson equation on a Riemannian submersion in a specific scenario if the potential vector field

ω

of the soliton is of gradient type =:grad

(γ)

and provide some examples of an

η

-RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

11 pages, 260 KiB

Open AccessArticle

Finsler Warped Product Metrics with Special Curvature Properties

Lingen Sun

Xiaoling Zhang

and

Mengke Wu

Axioms 2023, 12(8), 784; https://doi.org/10.3390/axioms12080784 - 12 Aug 2023

Viewed by 346

Abstract

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing

χ

-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the

χ

-curvature vanishes if and only if the H-curvature vanishes. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

18 pages, 326 KiB

Open AccessArticle

Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles

Esmaeil Peyghan

Davood Seifipour

and

Ion Mihai

Axioms 2023, 12(7), 667; https://doi.org/10.3390/axioms12070667 - 06 Jul 2023

Cited by 2 | Viewed by 594

Abstract

The purpose of this paper is to find some conditions under which the tangent bundle

T M

The purpose of this paper is to find some conditions under which the tangent bundle

T M

has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical distribution and the tangent bundle of a statistical manifold too. Moreover, we also study the mutual curvatures of a statistical manifold M and its tangent bundle

T M

and we investigate their relations. More precisely, we obtain the mutual curvatures of well-known connections on the tangent bundle

T M

(the complete, horizontal, and Sasaki connections) and we study the vanishing of them. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application II)

16 pages, 545 KiB

Open AccessArticle

Bertrand Offsets of Ruled Surfaces with Blaschke Frame in Euclidean 3-Space

Sahar H. Nazra

and

Rashad A. Abdel-Baky

Axioms 2023, 12(7), 649; https://doi.org/10.3390/axioms12070649 - 29 Jun 2023

Viewed by 421

Abstract

Dual representations of the Bertrand offset-surfaces are specified and several new results are gained in terms of their integral invariants. A new description of Bertrand offsets of developable surfaces is given. Furthermore, several relationships through the striction curves of Bertrand offsets of ruled [...] Read more.

(This article belongs to the Special Issue Differential Geometry and Its Application II)

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